A Two-Time-Scale Approach for Production Planning in Discrete Time

2005 ◽  
pp. 43-60
Author(s):  
Qing Zhang ◽  
George Yin
Keyword(s):  
Production Planning ◽  
Discrete Time ◽  
Time Scale

scholarly journals On time dependent multistep dynamic processes

1991 ◽  
Vol 43 (1) ◽  
pp. 51-61
Author(s):  
Ferenc Szidarovszky ◽  
Ioannis K. Argyros
Keyword(s):  
Topological Space ◽  
Discrete Time ◽  
Difference Equations ◽  
Time Scale ◽  
Time Dependent ◽  
Dynamic Processes ◽  
Monotone Convergence ◽  
Speed Of Convergence ◽  
Nonlinear Difference Equations ◽  
Ordered Topological Space

The discrete time scale Liapunov theory is extended to time dependent, higher order, nonlinear difference equations in a partially ordered topological space. The monotone convergence of the solution is examined and the speed of convergence is estimated.

Amplitudes of Composition Fluctuations in the Simplest Chemical Reaction Equilibrium

2004 ◽  
Vol 218 (9) ◽  
pp. 1033-1040 ◽  
Author(s):  
M. Šolc ◽  
J. Hostomský
Keyword(s):  
Random Walk ◽  
Discrete Time ◽  
Continuous Time ◽  
Time Scale ◽  
Numerical Study ◽  
Mean Amplitude ◽  
Time Interval ◽  
The Mean ◽  
Composition Fluctuations ◽  
Number Of Particles

AbstractWe present a numerical study of equilibrium composition fluctuations in a system where the reaction X1 ⇔ X2 having the equilibrium constant equal to 1 takes place. The total number of reacting particles is N. On a discrete time scale, the amplitude of a fluctuation having the lifetime 2r reaction events is defined as the difference between the number of particles X1 in the microstate most distant from the microstate N/2 visited at least once during the fluctuation lifetime, and the equilibrium number of particles X1, N/2. On the discrete time scale, the mean value of this amplitude, m̅(r̅), is calculated in the random walk approximation. On a continuous time scale, the average amplitude of fluctuations chosen randomly and regardless of their lifetime from an ensemble of fluctuations occurring within the time interval (0,z), z → ∞, tends with increasing N to ~1.243 N0.25. Introducing a fraction of fluctuation lifetime during which the composition of the system spends below the mean amplitude m̅(r̅), we obtain a value of the mean amplitude of equilibrium fluctuations on the continuous time scale equal to ~1.19√N. The results suggest that using the random walk value m̅(r̅) and taking into account a) the exponential density of fluctuations lifetimes and b) the fact that the time sequence of reaction events represents the Poisson process, we obtain values of fluctuations amplitudes which differ only slightly from those derived for the Ehrenfest model.

scholarly journals Asymptotic Convergence of the Solutions of a Dynamic Equation on Discrete Time Scales

2012 ◽  
Vol 2012 ◽  
pp. 1-20 ◽  
Author(s):  
J. Diblík ◽  
M. Růžičková ◽  
Z. Šmarda ◽  
Z. Šutá
Keyword(s):  
Time Scales ◽  
Discrete Time ◽  
Dynamic Equation ◽  
Time Scale ◽  
Asymptotic Convergence ◽  
Main Attention ◽  
All Solutions ◽  
Convergent Solution

The paper investigates a dynamic equationΔy(tn)=β(tn)[y(tn−j)−y(tn−k)]forn→∞, wherekandjare integers such thatk>j≥0, on an arbitrary discrete time scaleT:={tn}withtn∈ℝ,n∈ℤn0−k∞={n0−k,n0−k+1,…},n0∈ℕ,tn<tn+1,Δy(tn)=y(tn+1)−y(tn), andlimn→∞tn=∞. We assumeβ:T→(0,∞). It is proved that, for the asymptotic convergence of all solutions, the existence of an increasing and asymptotically convergent solution is sufficient. Therefore, the main attention is paid to the criteria for the existence of an increasing solution asymptotically convergent forn→∞. The results are presented as inequalities for the functionβ. Examples demonstrate that the criteria obtained are sharp in a sense.

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